Related papers: On the Word Problem for Compressible Monoids

Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…

Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…

The paper completely characterizes the primality of acyclic DFAs, where a DFA $\mathcal{A}$ is prime if there do not exist DFAs $\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) = \bigcap_{i=1}^{t}…

We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their…

We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic and machine-independent…

We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that…

In this article we provide a new perspective on the word problem of a group by using languages of nested words. These were introduced by Alur and Madhusudan as a way to model programming languages such as HTML. We demonstrate how a class of…

Word class flexibility refers to the phenomenon whereby a single word form is used across different grammatical categories. Extensive work in linguistic typology has sought to characterize word class flexibility across languages, but…

In 2007 it was conjectured that the Constraint Satisfaction Problem (CSP) over a constraint language $\Gamma$ is tractable if and only if $\Gamma$ is preserved by a weak near-unanimity (WNU) operation. After many efforts and partial…

A language is dense if the set of all infixes (or subwords) of the language is the set of all words. Here, it is shown that it is decidable whether the language accepted by a nondeterministic Turing machine with a one-way read-only input…

In this short note, we study C((t)) in the language of valued rings. We show that a definable subset of C((t))n (or in monster model, Mn) is definably compact iff it is closed and unbounded. Then we give some comments on definable groups…

We give lower bounds on the complexity of the word problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, Grigorchuk's group and Thompson's groups, we prove that their…

Let $w$ be a group-word. Suppose that the set of all $w$-values in a profinite group $G$ is contained in a union of countably many subgroups. It is natural to ask in what way the structure of the verbal subgroup $w(G)$ depends on the…

Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…

In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…

For two given $\omega$-terms $\alpha$ and $\beta$, the word problem for $\omega$-terms over a variety $\boldsymbol{\mathrm{V}}$ asks whether $\alpha=\beta$ in all monoids in $\boldsymbol{\mathrm{V}}$. We show that the word problem for…

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…

We present a necessary condition for an infinite language to be multiple context-free, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of the…

A group-word w is called concise if whenever the set of w-values in a group G is finite it always follows that the verbal subgroup w(G) is finite. More generally, a word w is said to be concise in a class of groups X if whenever the set of…